Spectral states in NS-LMXBs observed with MAXI/GSC and Swift/BAT
Kazumi Asai,1 Tatehiro Mihara,1 Masaru Matsuoka,1 and Mutsumi Sugizaki1

1

MAXI team, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198
E-mail(KA): kazumi@crab.riken.jp
Abstract

We review the spectral states in NS-LMXBs observed with MAXI/GSC and Swift/BAT. The spectral
state transitions (soft/hard) were seen in the NS-LMXB transients. This was caused by the instability in astandard accretion disk. Sensitive observations with GSC and BAT showed outbursts even with small peakluminosities and shorter durations. Such “mini-outbursts” were observed in four sources; 4U 1636−536,
4U 1705−44, 4U 1608−52, and GS 1826−238 (Asai et al. 2015). We understand it as a “purr-type” ofdisk instability predicted by Mineshige and Osaki (1985), whereas the large normal outburst is named
as a roar-type. There are several atoll NS-LMXBs, which are persistent and always in the soft state.
Although the hardness ratio (HR) in GSC and BAT observations is always low (i.e. soft state), the HR
distributed in two (higher/lower) groups. The higher group contains 4U 1820−30 and 4U 1735−44, while
the lower group contains GX 3+1, GX 9+1, GX 13+1, and GX 9+9. We interpreted the difference tocome from the size of the Comptonized cloud. The high HR was resulted from a large Comptonized cloud,which might be dammed at the Alfvén radius by rather high magnetic fields (Asai et al. 2016). In thebrightest NS-LMXB (Z sources), there are three branches; Horizontal Branch (HB), Normal Branch (NB)
and Flaring Branch (FB). Although the differences of HB and NB in the spectral and timing properties
indicated some changes in the geometrical structure, the physical understanding is still controversial. We
suggest that the difference of HB and NB might be explained by existing of the disk evaporation.
Key words: accretion, accretion disks — X-rays:neutron — X-rays:binaries

1.

Introduction

Low mass X-ray binaries with a weakly magnetized neutron star (NS-LMXB) are divided into two main subclasses (Z sources and Atoll sources) based on their behavior on the color–color the diagram and hardness–
intensity diagram (Hasinger & van der Klis 1989). Z
sources are generally bright and sometimes become close
to the Eddington luminosity (LE ). On the other hand,
Atoll sources are generally less bright, L ≤ 0.5 LE . The
NS-LMXBs show two kinds of X-ray spectra depending on their X-ray luminosities. In the high luminosity(> 1037 erg/s ) it is dominated by blackbody components,
and called the soft state. On the other hand, in the low
luminosity( < 5×1036 erg/s ) it is dominated by a Comptonized component, and called the hard state. Z sources
are usually in soft state, whereas some of Atoll sources
exhibit spectral state transitions (soft or hard).
The present study focuses on the properties of thespectral state of Z sources and Atoll sources. The analyzed data are MAXI (Matsuoka et al. 2009)/GSC (Gas

Slit Camera: Mihara et al. 2011; Sugizaki et al. 2011) 1
and Swift (Gehrels et al. 2004)/BAT (Burst Alert Telescope: Barthelmy et al. 2005) 2 . The obtained countrates of GSC and BAT were converted to luminosities
by assuming a Crab-like spectrum (Kirsch et al. 2005)
and the distances listed in table 1. The assumption of
Crab-like spectrum is acceptable in the hard state, because the energy spectrum is dominated by the Comptonized emission approximated by a power law with thephoton index of 1–2. On the other hand, in the soft
state, the energy spectrum is dominated by the thermal
emission. The obtained luminosity by assuming Crablike spectrum is underestimated in the 2–10 keV band,
but is overestimated in the 15–50 keV band. As a result,the hardness ratio (HR) of two energy bands is overestimated by 2.0 times (see Asai et al. 2015 for detail).
Therefore, we handle only the relative difference.
In this paper, first, we introduce two kinds of spectral state transitions, normal outburst and mini outburst*1 <http://maxi.riken.jp/>.
*2 <http://heasarc.gsfc.nasa.gov/docs/swift/results/transients/>.

Table 1. Distances used in this paper

Name
Atoll sources
Aql X-1
4U 1608−52
4U 1636−536
4U 1705−44
4U 1735−44
4U 1820−30
GX 3+1
GX 9+1
GX 9+9GX 13+1
GS 1826−238
XTE J1709−267
Z sources
Cyg X-2
GX 17+2
GX 340+0
Sco X-1
GX 5−1
GX 349+2

Distance (kpc)

Ref.∗

5
4.1
6
7.4
8.5
7.6
4.5
5
5
7
7
8.8

(1)
(2)
(1)
(1)
(2)
(1)
(3)
(1)
(4)
(1)
(1)
(1)

7.2
12.6
11
2.8
9.2
5

(1)
(5)
(4)
(1)
(4)
(4)

∗ (1) Liu et al. (2007), (2) Galloway et al. (2008), (3) Kuulkers and van der Klis (2000), (4) Christian and Swank(1997), (5) Lin et al. (2012).
2. Two kinds of spectral state transitions
We define the spectral state with MAXI/GSC (2–10 keV)and Swift/BAT (15–50 keV). First, we make the histograms (number of days) of the BAT/GSC hardness
ratios (HRs) of the seven NS-LMXBs (4U 1636−536,
4U 1705−44, 4U 1608−52, GS 1826−238, Aql X-1,
XTE J1709−267, and 4U 1820−30). We basicallyadopted the HR of the lowest point between the two
peaks as the threshold between the soft and hard states(see table 2 in Asai et al. 2015). Figure 1 shows the GSC
light curve, BAT light curve, and HRs (BAT/GSC) of
4U 1705−44. In this figure, the threshold separate thedata points into soft and hard states.
From the light curve, we noticed that the soft states
are separated into two luminosity classes. Comparing
with the average luminosity of soft state, one is above

BAT/GSC LBAT(erg s−1) LGSC(erg s−1)

(Asai et al. 2015). Next, we show two groups in a soft
state of Atoll sources, and then propose that the difference would come from the surface magnetic field of aneutron star (Asai et al. 2016). Finally, we discuss thedifference between Horizontal and Normal branch (HB
and NB) of Z sources. We suggest that the difference
might be explained by the disk evaporation.

4U 1705−44

1038
1037
1036
35
1037
10

1036
1035
1
0.1
0.01
55000

55200

55400

55600

55800

56000
MJD

56200

56400

56600

56800

Fig. 1. One-day light curves (LC) of 4U 1705−44 shown as an example. Top: GSC LC in the 2–10 keV band. Middle: BAT LC in the
15–50 keV band. Bottom: the hardness ratios (HRs) (BAT/GSC).
Vertical error bars represent 1 σ statistical uncertainty. Circles andtriangles represent data of soft and hard states, respectively. See
Asai et al. (2015) for other sources.

ten to 1037 erg s−1 , the other is below this value. So, we
calculated the average 2–10 keV luminosities of the softand hard states using the thresholds of the HR for sevensources. The soft states of all seven sources are separated
into two luminosity classes. If the average luminosity inthe soft state is below ∼ 1037 erg s−1 , the X-ray variability (repeated small increase) is called “mini-outbursts,”
whereas outburst with average luminosity above ∼ 1037
erg s−1 is called “normal outburst.” The mini-outbursts
were characterized by smaller amplitudes and shorter
duration than those of normal outbursts. Such minioutbursts were observed in the four sources (4U 1636–
536, 4U 1705–44, 4U 1608–52, and GS 1826–238). We
consider that the light curve of mini outburst is similar
to the calculated light curve for a “purr-type” of disk
instability predicted by Mineshige and Osaki (1985).
Normal outbursts in NS-LMXBs are usually interpreted by the disk instability model like the outburstof dwarf novae. In this model, local disk instabilities(S-shaped curves in the surface density and mass accretion rate diagram) are caused by the partial ionizationof hydrogen and helium. The theoretical disk instability model of Mineshige and Osaki (1983, 1985) predicts
both large-amplitude outbursts (roar type) and smallamplitude variability (purr type). The former is considered to correspond to normal outburst, but no correspondence has been found for the latter. Here, we proposethat purr-type outbursts correspond to mini-outbursts,
because the characteristics (small-amplitude and shortduration) of both types are quite similar.
The main difference between two types (roar type andpurr type) is α parameter of the standard disk. The αparameter is usually considered to depend on the disk
temperature. In order to explain a normal outburst,
two S-curves with a different α values are used. As aresult, the width of the middle branch of S-curve is extended. This means that the instability can propagate
through the whole disk, and then outburst occurs. Thisis a roar type. In the case of one S-curve, the widthLuminosity (1036 erg/s)

100

(a)

(b)

(c)

4U182010

GS1826
4U1636

1
109

1010
1011
Disk radius (cm)Aql X−1
4U16081012

Fig. 2. Average X-ray luminosity in the 2–10 keV band as a functionof outer disk radius. Open circles and filled triangles represent
data of soft and hard states, respectively. Theoretical lines of (a),(b), and (c) are calculated by equation (53) of Tuchman et al.
(1990) (C = 10−4 ). The irradiation temperatures of (a), (b),and (c) are Tirr = 10000 K, 5000 K, and 3000 K, respectively.

of the middle branch is narrow, and then the instability
propagates only a part of the disk. This is a purr type.
We considered that mini outburst occurs when the middle branch is narrow. Tuchman, Mineshige, and Wheeler(1990) reported that the middle branch can become narrow, when the disk is irradiated by the central sources.
So, we investigate the status of the outer disk, assumingthat the disk temperature is determined by X-ray irradiation. Figure 2 shows the average X-ray luminosities
and the outer radius of the accretion disk. Here, theouter radius was assumed as 0.35 of the binary separation (Smak 1982, and see Asai et al. 2015 in detail). For
4U 1820−30, we interpreted the spectral state transitionas other type because average luminosity in both soft andhard state are above ∼ 1037 erg s−1 (see Asai et al. 2015
in detail). The left side of (a) indicates a stable region,
where S-shape disappears. The right side of (c) is an
unstable region, where a normal outburst occurs. In theregion between (a) and (b), we observed mini-outbursts.
Therefore, we interpreted mini-outbursts were caused by
X-ray irradiation.
3. Hard tail emission in Atoll sources
Average hard-tail X-ray emission in the soft state of ninebright Atoll source (Aql X-1, 4U1608−52, 4U1705−44,
GX 3+1, GX 9+9, GX 13+1, GX 9+1, 4U 1735−44,
4U 1820−30) are investigated by using the light curves of
MAXI/GSC and Swift/BAT. Two sources (4U 1820−30
and 4U 1735−44) exhibit large HR (15–50 keV/2–
10 keV: HR > 0.1), while the other sources distributeat HR ≤ 0.1. In either case, HR does not depend on
the 2–10 keV luminosity. Therefore the difference of
HR is due to the 15–50 keV luminosity, which is Comp-

tonized emission. The Compton cloud is assumed to bearound the neutron star. In general, Comptonized emission is considered to be affected by the inclination, originof seed photon, and electron temperature of Compton
cloud. However, we cannot see a clear difference of any
parameters between two groups from the results by several authors (see Asai et al. 2016). So, we propose thatthe difference between the two groups would be due tothe size of the Compton cloud. The group with high HR
would have large Compton cloud. Next, we consider thelocation of Compton cloud.
In the soft state, the location for Compton cloud iscontroversial. Here, let us take into account of the magnetic field of the neutron star. The magnetic field of aneutron star in LMXB is considered to be weak. However, in some cases, the effect of the magnetic field istaken into account. In the soft state, most of the gas in
the disk accretes onto the neutron star, because the disk
can extend to the neutron star or ISCO. The accretion
flow is thermalized on the surface, and the emission fromthere is Comptonized by the plasma around the neutronstar. However, if the magnetic field of the neutron staris relatively strong, the Alfvén radius would be larger
than the ISCO. In this case, the accretion flow would be
stopped and spread around the Alfvén radius, and thenthe relatively large Compton cloud would be created.
We calculated the Alfvén radius as a function of luminosity (see figure 7 in Asai et al. 2016). Here, we adopted
a gas pressure dominant accretion disk. When L is1037 erg s−1 , RA is larger than ISCO for B > 1.5×108 G.
In this case, the accretion flow would be stopped andspread at the Alfvén radius, and then the relatively large
Compton cloud would be created. As a result, the HR
would be large (for example HR > 0.09). On the other
hand, when B < 1 × 108 G, the RA is smaller than both
ISCO and NS surface. In this case, the accretion flow is
not affected by the magnetic field, and then most of thegas in the disk accretes onto the NS equatorial region.
The HR would be low (for example HR < 0.09). According to increasing the luminosity, RA becomes smaller andthe size of Compton cloud would be smaller.
By attributing the difference of the size of Compton
cloud to the Alfvén radius, we can estimate the magnetic
fields of neutron star. Since HR of 4U 1820−30 and
4U 1735−44 is large, Bs is estimated as B ≥ 2.5×108 G.
The upper limit of B is given for other seven sources.
These results are consistent with the previous results.
4.

Transition between Horizontal Branch and Normal
Branch in Z sources
We investigated long-term variations in the hardnessluminosity diagram (HLD) of six Z sources by using
MAXI/GSC and Swift/BAT. We confirm the secular motion of the Z-pattern through the HLD in four sources

r

1

(3)

R_c

P1

0.5
R
(1)

P2

_A

0.2

A
R_

Mdot [Eddington]

2(2)

The change of transition luminosity with the luminosity decreasing caused the shift of Z-pattern from Cyglike sources to Sco-like sources. The inner disk radius
becomes smaller as the transition luminosity decreases(Lin et al. 2009). Assuming that the large inner disk
radius (∼ 20 km) of Z sources represent the Alfvén radius of the neutron star with the surface magnetic fieldof ∼ 109 G, the change of transition luminosity can be
attributed to a gradual change of accretion disk fromthe radiation-pressure-dominated disk to gas-pressuredominated disk. At the highest luminosity, the Z-patternshows Cyg-like with a long HB. At low luminosities, it
becomes Sco-like with a short HB. Figure 19 in Lin etal. (2009) shows the change of the inner disk radius at
the transition point of HB and NB. The radius increases
from Sco-like to Cyg-like. Here we consider the possibility of which the Alfvén radius determines the inner radius. We calculated Alfvén radius is for two special cases.
At high luminosity, the disk would be dominated by theradiation pressure [(1)R A line in figure 3]. On the other
hand, the lowest luminosity in Sco-like, the disk would be
gas pressure dominated [(2)R A line in figure 3]. Here,we consider the possibility of disk evaporation. Whenthe radiation pressure overcomes gravitational force, thedisk evaporation would occur. So, we also calculated theevaporation radius [(3)R cr line in figure 3]. When thesource is bright (Cyg-like), the inner radius moves along(1)R A line. This is the HB of Cyg-like. When the massaccretion rate reaches the evaporation line of (3)R cr,
evaporation starts (point P1). After then, the inner radius moves along (3)R cr. This is the NB of Cyg-like.
In a bright Cyg-like, the inner radius is large and theevaporation point is at high luminosity. As a result, the
HB is long. In a low luminosity as Sco-like, the disk becomes gas pressure dominate and the Alfvén radius (i.e.
inner disk radius) is shown as (2)R A line. In this case,the HB is short and the transition occurs at lower lu-

ISCO(Sco X-1, GX 17+2, Cyg X-2, and GX 5−1). Especially,
location of the HB and the NB shifted in the time scale ofseveral hundred days. Also, a transition luminosity from
HB to NB changed with the shift. We propose a simple
model of transition between HB and NB. Since the luminosity is close to the Eddington luminosity, the innerpart of the accretion disk is considered to be a radiationpressure-dominated disk. When the luminosity is evenhigher, the radiative force overcomes the gravity on thesurface of the accretion disk, and the surface starts toevaporate. We interpret that the difference of HB and
NB comes from the existence of the evaporation. In the
HB, the evaporation does not occur yet, because the luminosity is comparably low. When the source reaches atransition luminosity from HB to NB with the luminosity increasing, the disk evaporation will start. Namely,
the evaporation will occur in NB.

0.1
10

20
Radius [km]50

Fig. 3. The Alfvén radius (1) and (2) for B = 109 G (Campana etal. 1998), and the critical radius (3) (Fukue 2004) as a functionof the accretion rate. (1) is for radiation pressure dominated disk[equation (18) in Campana et al. 1998] and (2) for gas pressure
dominated disk [equation (14) in Campana et al. 1998].

minosity (point P2). In summary, we suggest that thedifference of HB and NB might be explained by the disk
evaporation.
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